The motion of constrained System may be described in terms of non-indepen- dnt Sate functions. (the Lagrangian may be involving any order derivatives). We considered the change of the action integral and constraint equations under the infinitesimal transformation of the time-space points and stale functions of constrained System. This lead to general transformation results. Along the trajectory of the motion of constrainedsystem

We obtained the transformation properties of that system: From which we can give generalized Killing's partial differential equations. The transformations generated by the solutions of genera- lized Killing's equations

which may yield classical Noether's Conservation quan- tities. We have considered the time-space and internal transfor mations of continuous constrained system which leave the constraint conditions invariant and given a necessary and sufficient conditions that transformations may yield conservation current. The application to generalized and Classical mechanics is discussed detail and Some illustratious for Solution of generalized Killing's equations are given.